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Asymptotics of an optimal compliance-location problem

Published online by Cambridge University Press:  11 October 2006

Giuseppe Buttazzo ,
Filippo Santambrogio  and
Nicolas Varchon
Giuseppe Buttazzo
Affiliation:
 Università di Pisa, Dip. di Matematica, Largo B. Pontecorvo, 5, 56127 Pisa, Italy; buttazzo@dm.unipi.it
Filippo Santambrogio
Affiliation:
 Scuola Normale Superiore, Classe di Scienze, Piazza dei Cavalieri, 7, 56126 Pisa, Italy; santambrogio@sns.it
Nicolas Varchon
Affiliation:
 Collège Condorcet de Bresles, 60510 Bresles, France; nicolasvarchon@netscape.net
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Abstract

We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

Keywords

Complianceoptimal locationshape optimizationΓ-convergence.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 4 , October 2006 , pp. 752 - 769
Copyright
© EDP Sciences, SMAI, 2006

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